An automatic core setting machine is disclosed in U.S. Pat. No. 4,590,982. In that machine the cores are carried in pockets in a mask which places the cores in the cavities of the moulds. Typically the cores are held by vacuum. The apparatus is suited for placing cores in moulds that have upwardly opening mould cavities. Hereto the core mask is swung downwardly and laterally through a short arc from a core-loading position to a pre-setting position and then is lowered vertically to a core-releasing position to place the cores in the mould. When the mask is in its loading position, its pockets face away from the mould station to enable the cores to be loaded in the pockets from the side of the machine. In order to carry out the combined rotational, lateral and vertical movement, the mask holder is guided by a complex linkage mechanism. Core placing must, however, be precise and requires relatively high forces for pressing the cores into the mould cavities. Moreover, the forces must not deform the construction since this could lead to core fracturing. It is very difficult to fulfil these criteria with the complex linkage mechanism of the known core-setting machine.